Oracle Blog

Monday Jun 18, 2007

A few years ago, after a long day (for a fifth grader) of studying
long division, my daughter exclaimed that she saw no practical use
for remainders. It reminded me of a similar day, sitting in a
computer science class on computational complexity, of feeling that
there was no practical use for
knapsack problems. Both, it turns
out, are the basis for many of the cryptography systems in vogue
for online security and identity based systems. The exponential
complexity that makes a
problem intractable also makes it stronger
in the face of brute-force attack, and the use of remainders
(particularly the
Chinese remainder theorem) makes it practically computable.
Realizing that Professor Steiglitz was most egregiously correct
(back in 1983) when he warned us that large prime numbers were in
our futures, remainders, NP-complete problems and computational complexity
all go "click" when I'm indulging my eBay habit.

Fast forward a few years: large-scale compute grids enable brute-force
attacks against weaker (shorter key length) crypto systems, and
increasing the key length to stay one or two hops ahead of the bad
guys means additional drains on power, performance and time. Particularly
bad things if you're worried about securing a data path to your mobile
device, where power and time equal battery life. What's needed is a crypto
system that uses shorter key lengths to produce a stronger system, and
the click-fitting math this time are elliptic curves, providing
a more efficient way to tackle the factoring problems underlying crypto
systems. The result - elliptic curve cryptography - is a promising
step in making systems more efficient and secure at the same time.

Aside from reading Simon Singh's
Fermat's Enigma, which neatly tied together modular forms, elliptic curves,
Fermat's Last Theorem, and Princeton University, I am, in the words of
Napoleon Dynamite, in the need of some skills. For higher math, bigger
invention and practical applications of all of the above, I had Sun Labs
Distinguished Engineer Vipul Gupta join me for our Innovating@Sun podcast on
Cryptography Breakthroughs. It's the current equivalent of being
told that large prime numbers are in your future.